From the intimate connexion of the present subject with the improvement of the Achromatic Telescope, it must be admitted to be one of the most important in Optics; while, from the minuteness of the effects which are to be observed and compared, it is unquestionably one of the most difficult. From this cause very little progress has been made in the investigation. The irrationality of the coloured spaces, in prismatic spectra, formed by different substances, has not even been mentioned in any of our elementary treatises on Natural Philosophy, and there are some philosophers who have scrupled to receive it as a truth established in Physics.

It will be readily admitted by every person who has been accustomed to solar observations, that an apparatus for diminishing the intensity of the sun's light, without distorting or colouring the resulting image, is still a desideratum in Practical Astronomy.

Dr Herschel is the only person who has given any degree of attention to this subject. When he applied his powerful telescopes to examine the surface of the sun, he found that the ordinary method of attenuating the light by smoked or coloured glasses, was of no avail; and it was in the prosecution of his experiments for determining the relative advantages of differently coloured glasses, or of combinations of differently coloured glasses, that he was conducted to those splendid discoveries respecting the invisible rays, which have formed an epoch both in Chemistry and Optics.

Explosions in mines, from the kindling of the inflammable gas called Fire-Damp by the miners, have always occasionally occurred. Of late they have become more frequent in some of the coal-mines in this country, particularly those in the districts of the Tyne, and the Wear, in the North of England, and have been attended with such fatal consequences, as to have forcibly called public attention to the subject. In an explosion in one mine, about two years ago, ninety-two persons were killed; in another, which occurred soon after, thirty-two lost their lives; in one which happened within these few months, fifty-seven persons were destroyed; and recently, it has been affirmed, that several hundred lives are lost annually from this cause. From the state of the mines, particularly in the accumulation of wastes, the collection of water, and the increasing depth of the workings, there is reason to fear, too, that such accidents will become more frequent. Humanity loudly calls, therefore, on every effort being made to obviate the calamity; and even as a national concern, the immense loss of property in the mines, and the probability which has been suggested, that the working of them must ere long be abandoned, give to the subject the highest claims to consideration.

The divisions of the day which different nations have employed, are denoted by hour-lines of various kinds on the sphere. Of these hour-lines, drawn on a supposition that neglects the inequalities of the Earth's motion, there are three kinds.

The first kind denotes hours counted from the meridian, equal to each other at all declinations of the sun. These lines are great circles on the sphere, passing through the poles of the equator, and every pair intercepting a similar arc on each of the parallels. Of this kind are the hour-lines of sidereal time, counted from the meridian, and the hour-lines of solar time, counted from the meridian.

As far as we can judge from historical records, the primeval mode of disposing of dead bodies, was by inhumation. It has been observed in another essay, that according to Pliny, the ancient Romans did not burn their dead, but consigned them to the earth. It must be admitted, however, that by some the mode of cremation had been preferred in a very early period of their history; as we cannot otherwise account for the prohibition, which Plutarch ascribes to Numa, as to the burning of his body.

The following circumstances respecting the Blind and Deaf Boy, James Mitchell, have come to my knowledge since the publication of Professor Stewart's Memoir; and I doubt not but the Society will think them worthy of being recorded. They are derived from the most accurate and authentic of all sources, the boy's sister, Miss Mitchell.

In the month of April 1814, Mr Parker, an English gentleman, (distinguished, as I have since learned, for his active benevolence,) did me the honour to wait upon me, to communicate a plan for the instruction of young Mitchell, which had some time before occurred to him, and which he was very desirous should be put to the test of experiment. This method seemed in no respect inconsistent with those principles which in all circumstances appear to regulate the acquisition of language; and I therefore expressed my willingness, to promote, by every means in my power, the object which Mr Parker had in view.

The practicability of instructing in any kind of language a person blind and deaf from infancy seems not to have occurred to the friends of James Mitchell till suggested by Dr Gordon, whose ideas on the subject are contained in Professor Stewart's account published in the Transactions of this Society. An attempt has been since made to put in practice a plan for the same purpose, proposed by Mr Parker, an English gentleman who resided for a short time in Scotland. This consisted in accustoming him to handle the letters of the alphabet, formed of pieces of wood or paste board, when placed together so as to compose different words significant of tangible objects, and making him handle the objects in order to learn their meaning.

It has long ago been remarked by the Abbé Hauy, that the property of Double Refraction is not possessed by any of those crystals the form of whose integrant molecule is distinguished by its symmetry, such as the Cube and the Regular Tetraedron. This class of minerals comprehends Fluate of Lime, Muriate of Soda, Spinelle Ruby, Muriate of Ammonia, Alum and the Diamond; and though M. Hauy had examined only a very small number of doubly refracting crystals, yet, with the exception of the Diamond, which I have found in many cases to possess the property of Double Refraction, his remark was confirmed by the experiments of Malus, Biot and myself, who considered all the crystals of this class as exercising no more action upon polarised light than a mass of water.

It has been long known to those who have studied the optical properties of Calcareous Spar, that there are numerous specimens of that mineral which form a multiplicity of images, affected with the most brilliant colours. These colours were considered by Malus, and other philosophers, as the colours of thin plates, and were supposed to be produced by a film of air, included in accidental fissures or fractures within the crystal. I have already shewn, from numerous experiments, that this opinion is erroneous, and that the various colours with which the images are affected, arise from the transmission of polarised light, through an extremely thin film or stratum of calcareous spar, which has different thicknesses in different specimens, but which has an invariable position, being always parallel to a plane passing through the longer diagonals of the rhomboidal faces.

The descriptions which historians and geographers have transmitted to us of the ancient world, are not generally deficient either in copiousness or accuracy. The theatre of those great events, which still interest mankind, may be commonly ascertained with sufficient precision. The distinct knowledge of the ancients, however, was limited to a certain sphere; after passing which, clouds always begin to envelope it. The almost total change of names, the uncertainty as to their itinerary measures, and the defects of their mathematical geography, leave no perfectly fixed point on which we can rest.

The composition of Sea-Water has been variously stated by different chemists, not only with regard to the proportions of the salts which it holds in solution, but with regard even to the ingredients themselves.

According to Lavoisier, it contains muriate of soda, muriate of magnesia, and muriate of lime, sulphate of soda, sulphate of magnesia, sulphate and carbonate of lime. The proportions he assigns are, in a pound of water, (French weights) 126 grains of muriate of soda, 14¾ grains muriate of magnesia, 23 grains muriate of lime mixed with muriate of magnesia, 7 grains of sulphate of soda and sulphate of magnesia, and 8 grains of sulphate and carbonate of lime.

It is well-known as a fundamental principle in statics, that “Two pressures, represented in direction and quantity by “two adjoining sides of a parallelogram, are equivalent to one “represented in direction and quantity by the diagonal “which passes through the point at which these sides meet.” A demonstration of this proposition, that shall be at once sufficiently concise, and sufficiently elementary, to admit of its being with propriety introduced into a course of academical instruction, has been hitherto, so far as I know, a desideratum. The following may perhaps be found to possess that advantage.

My Dear Brother,

The inclosed account was drawn up at the request of Robert Græme, Esq. when all the circumstances were fresh in my own recollection, and that of all with whom I had occasion to confer on the subject. Since you requested me to send you a correct copy of the whole case, I have renewed my inquiries among the friends of the young woman, and submitted my account to several persons, who were most capable of supplying any omissions, or correcting any mistakes. I can confidently vouch for the general accuracy of the statement; but would not wish its credibility to rest entirely on my single testimony.

The analysis of Mineral Waters has always been considered as a difficult operation. Numerous methods are employed to discover their ingredients, and estimate their quantities, many of which are liable to errors. This diversity of method itself is a source of discordant results. And to those not familiar with such researches, it presents the difficulty often of determining what process is best adapted to discover a particular composition. Hence the advantage of a general formula, if this could be given, applicable to the analysis of all waters. The views which have been stated in the papers, connected with this subject, which I have had the honour of submitting to the Society, have suggested a method which appears to me to admit of very general application, and to be simple, not difficult of execution, nor liable to any sources of error but what may be easily obviated. The principles on which this method is founded, and the details of the process itself, form the subject of the following observations.